Perimeter of hexagon -x + 11

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chavez0

10.10.2022

Mathematics

$a_{n}=-5(-3)^{n-1}$

Step-by-step explanation:

A geometric sequence or progession is defined as a sequence where each term can be found by multiplying a factor with the first term.

In this case, the first term is -5, the second term is 15 and the third term is -45.

$a_{1}=-5\\a_{2}=15\\a_{3}=-45$

To find the factor, we divide the second term by the first, and the third term by the second.

$\frac{15}{-5}=-3$

$\frac{-45}{15}=-3$

As you can notice, the factor is -3, so r=-3 .

Now, the explicit formula of this sequence can be found with

$a_{n}=a_{1}r^{n-1}$

Where refers to the n-th term.

Replacing values, we have

$a_{n}=-5(-3)^{n-1}$

Therefore, the explicit formula of the geometric sequence is

$a_{n}=-5(-3)^{n-1}$

Which can be used to find any other term in the sequence.

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